§10.60(ii) Duplication Formulas

Notes:

For (10.60.4) set 𝒞ν=Yν,
u=v=z, ν=-n-12, and α=π in
(10.23.8).
Then refer to (10.47.3), (10.47.4), and
also apply the following results obtained from Table 18.6.1:
Ck(-n-12)⁡(-1) equals
(2⁢n+1)!/(k!⁢(2⁢n+1-k)!) when k=0,1,…,2⁢n+1, and
equals 0 when k=2⁢n+2,2⁢n+3,….
For (10.60.5) use the same procedure, but with
𝒞ν=Jν.
Lastly, (10.60.6) follows by combining (10.60.4)
and (10.60.5) with §10.47(iv).